Journal of the Scientific Agricultural Society of Finland Vol. 54: 165-223, 1982 Maataloustieteellinen Aikakauskirja MEASURING TECHNOLOGICAL CHANGE IN AGRICULTURE AN APPLICATION BASED ON THE CES PRODUCTION FUNCTION Selostus: Teknologisen muutoksen mittaaminen maataloudessa CES-tuotantofunktioon perustuva sovellutus KALEVI HEMILÄ Ministry of Agriculture and Forestry, SF-00170 Helsinki 17, Finland Academic Dissertation TO BE PRESENTED, WITH THE PERMISSION OF THE Faculty of Agriculture and Forestry of the University of Helsinki, for public criticism in Auditorium XII on January 21, 1983, AT 12 O’CLOCK. SUOMEN MAATALOUSTIETEELLINEN SEURA HELSINKI https://www.c-info.fi/en/info/?token=pV_ycti3b6QyHz8m.zKI8LDDUr01xQXOyd0cLQw.XV6erHn26hnceYhyGrjbBgsY691Waxq5lyrM6NxDo_OviZ7FoVPSJR7SbDWqSm4MITmwnp1vj9BNDRo_ERYkvdygkysZd-9aJh4YxCfjRTDfzXgVryl8jdbHKCRl2f7fQ86lOd_SvG51iBgv2iCq8FZH2TH4uzhFivyqi7cUVgk Preface Most of the present study was carried out while I was employed at the Agricultural Economics Research Institute. 1 wish to express my sincere gratitude to Professor MATIAS TORVELA, Head of the Institute, for his encouragement and for placing the facilities of the Institute at my disposal. I owe a debt of gratitude to my teacher. Professor VILJO RYYNÄNEN, for the support he has given me in my work over a long period of time. His guidance and the interest with which he shared the numerous problems I faced in the course of my research work were crucial to the completing of this study. My special thanks are also due to Professor RISTO IHAMUOTILA for his support, advice and our discussions, which have been of great benefit to me. He has also given me confidence and courage, without which I would not have been able to finish this study. 1 also wish to thank Professor LAURI KETTUNEN, Head of the Marketing Research Department of the Institute, and other colleagues at the Institute who helped in different ways to bring this study to a conclusion. Mrs. BIRGIT HAGGREN and Mrs. RITVA HEIKKILÄ helped me in translating the text. PHILIP MASON, B.Sc. and THE ENGLISH CENTRE revised the English text. Mr. JANNE PINOMAA provided substantial assistance in solving the computational problems. Special thanks also to Miss HELENA KOIVULA for typing the manuscript and Miss MERJA MANNINEN for drawing the numerous figures. The support and encouragement of some of my closest friends have been very important to me. Therefore I wish to thank MATTI ylätalo and MIKKO SIITONEN. This study was supported by grants from the KYÖSTI HAATAJA FOUNDATION and the FINNISH CULTURAL FOUNDATION. I am grateful to the Scientific Agricultural Society of Finland for including this study in their series of publications. Finally, I wish to express my sincere thanks and gratitude to my wife for her interest and patience during my work. Helsinki, November 1982 Kalevi Hemilä 169 CONTENTS Abstract 171 Introduction 171 1. Technological change 173 1.1. The concept 173 1.2. Characteristics of technological change 175 2. Flow technological change occurs 178 2.1. Forms of technological change 178 2.2. Different trends in technological change 181 2.3. The effect of technological change on the optimum level of production 185 3. Measurement of technological change 187 3.1. Different lines of measuring 187 3.1.1. Measuring methods based on a production function 188 3.1.2 Measuring methods based on indices 190 3.2. Some methods for measuring technological change 191 3.2.1 Arithmetic and geometric indices 191 3.2.2. Production functions 192 3.2.2.1. The Cobb-Douglas function 192 3.2.2.2. The CES function 193 3.3. Practical applications of the measurement of technological change - previous studies 195 4. The method and statistical data used for empirical research 200 4.1. The method of empirical research 200 4.2. Estimation of the parameters of the CES function 200 4.3. Statistical data 202 4.3.1. General 202 4.3.2. Selection of variables 203 4.3.2.1. Output 203 4.3.2.2. Labour and capital inputs 204 4.3.2.3. Compensation paid to labour and capital - the income shares of labour and capital 206 5. Results 207 5.1. General 207 5.2. Results of the first stage of the analysis 208 5.2.1. The elasticity of substitution 210 5.2.2. The income share parameter and the capital intensity 212 5.3. Results of the second stage of the analysis 213 5.3.1. Technologically determined returns to scale 215 5.3.2. The efficiencyparameter 215 6. Conclusions from the effects of technological change on the development of agricultural production 216 7. Summary 218 REFERENCES 220 SELOSTUS 223 171 JOURNAL OF THE SCIENTIFIC AGRICULTURAL SOCIETY OF FINLAND Maataloustieteellinen Aikakauskirja Vol. 54: 165-223, 1982 Abstract. The purpose of this study is to analyse and measure the technological change that has occurred in agriculture. The study is primarily methodological with the focus on development of a method for measuring technological change and on testing this method. The study is divided into a theoretical and an empirical part. The most common methods for measuring technological change are examined in the theoretical part of the study together with the concepts connected with a technological change and its characteristics. The empirical part tests the applicability of the measuring method based on the CES function for estimating the parameters of technological change in agriculture. To a great extent the parameter estimates calculated conform with what was anticipated. Technological change will continue to be a very important source of productivity growth. By adapting to new technology our small farms can develop very fast in terms of structure and productivity. It appears that technological development will continue to proceed along the lines described in this study in the near future. Technological change can be expected to be capital-using and labour-saving. It will also have a considerable influence on increasing output, especially in cattle husbandry. Introduction The earliest developmental stage in agricultural production technology can be called the period of muscular labour. Agriculture based on muscular labour can be characterized in the following way. The majority of the population earns its living directly from agriculture. Production is largely non-specialized, and rural families produce foodstuffs and raw materials primarily to satisfy their own needs and to obtain the inputs required for further production. Tools - hoes, wooden ploughs and sleds - are made by agricultural producers themselves. The only source of power in agricultural production is human labour or animal power. The yield per unit area and per capita is low. Trade with other branches of the economy is restricted. Capital inputs are used very little (YUDELMAN et al. 1971, p. 136). Some progress was made as early as the period of muscular work. SCHAEFER-KEHNERT (1961, p. 219) considers the introduction of draught animals, the wheel and plough in agricultural production the first step towards technological development. HAYAMI and RUTTAN (1971, p. 27) state that growth in agricultural production based on muscular work amounts to an average of one per cent annually over the long term. They use this statement to refute the argument that traditional agriculture is perfectly static. Changes and growth are merely very slow. The industrial revolution, which began in the 18th century, led to the next 172 stage in the development of the industrializing countries. The division of labour and specialization between the various fields of the economy followed industrial growth. This also meant that agriculture was offered an increasing amount of inputs of industrial origin. This is how mechanization began. Although industrialization was rapid and the prices of industrially man- ufactured tools dropped, not all of them could be used in agriculture. According to SCHAEFER-KEHNERT (1961, p. 219), this was due to lack of suitable draught power. New machines were not of any significanthelp when animal power was used. Because of its heavy weight the steam engine was unsuitable for use on fields, though it was the basic machine in industry. It was not until the combustion engine was invented and mounted in a tractor that equipment produced by industry could be utilized by agriculture, thanks to sufficient draught power. Because the energy economy was in a crucial position when this change occurred, the new phase can also be called motorization. The introduction of the tractor into agriculture caused a noticeable reduction in the need for labour. In the diminishing rural population, true, it is hard to distinguish between the effect of the decreasing need for agricul- tural workers and that of the growing demand for industrial labourers. Both of them acted and still act side by side and exert an effect in the same direction. Increased productivity created by new technology has long been studied in economics. As early as the 1940 s it was observed that an increase in capital input alone cannot explain the rise in labour productivity (e.g. TINBERGEN 1942, TINTNER 1944). However, economic theory was still, roughly speak- ing, based on the assumption that the main factor influencing the growth of labour productivity is growth in capital input. The article by Moses Abramowitz in 1956, ’’Resource and Output Trends in the United States since 1870” (ABRAMOWITZ 1956) is considered an important step towards a detailed theoretical study and an empirical mea- surement of the factors that affect growth in productivity. There he proposed that the growth in output per unit of labour input is significantly greater than the growth in capital input he had measured. Abramowitz calls the ’’factor” that has - together with capital input - such an important effect on economic growth ’’the Residual”. Abramowitz characterizes the problem in the follow- ing way: ’’Since we know little about the causes of the Residual, the indicated importance of this element may be taken to be some sort of measure of our ignorance about the causes of economic growth in the United States and some sort of indication of where we need to concentrate our attention”. After the publication of Abramowitz’ article, empirical studies made by several researchers (e.g. SOLOW 1957, MASSELL 1960, KENDRICK 1961) have shown that in Western economies the growth in capital input is about half of the growth in labour productivity, or as low as only 10 % according to some researchers. Several studies found it surprising that greater attention had not been given to this ’’factor”, which together with capital input, so strongly affects economic growth. Abramowitz’ article started a new discussion about what this residual - as Abramowitz and several other researchers called it or 173 technical change by SOLOW (1957) or technological change by DOMAR (1961) - includes and what the quantities of its components are. During the past two decades literature on technological change has become comprehensive. Different methods have been developed to measure technological change and its components and to estimate its effects. The purpose of this study is to analyse and measure the technological change that agriculture has undergone. The first part of the study is a fairly comprehensive review of the theory and terminology on technological change. In the framework of the theory, the empirical part of the study makes an effort to analyse the tehnological development of Finnish agricul- ture. Here it is examined mainly as a problem of measurement. A solution is sought through production functions. The main interest is focused on measuring the characteristics of technological change. The goal of the empiri- cal part of the study is to develop a method based on a production function for measuring technological change and to test it in different kinds of agricultural enterprises using the results from bookkeeping farms. 1. Technological change 1.1. The concept The New Encyclopedia (ANON 1974) defines the concepts technique and technology in the following way: ’’Technique is the practical utilization of theoretical knowledge in material production, the science of engineering; in a wider sense knowledge of and skill in using labour saving methods. Being a theoretical concept, technique approaches technology. Technology is a common name for sciences which deal with technical systems and methods; it is a doctrine of the methods by which raw materials are worked into processed goods”. According to JANTSCH (1967, p. 15), technology means utilization of applied sciences; of natural, humanistic and social sciences. Technology includes the entire concept technique together with medicine, the science of agriculture and forestry, management science, etc. ’’Technology is systematic knowledge and action, usually of industrial processes but applicable to any recurrent activity. Technology is closely related to science and to engineering. Science deals with man’s understanding of the real world about him - the inherent properties of space, matter, energy and their interactions. Engineering is the application of objective knowledge to the creation of plans, designs, and means for achieving desired objectives. Technology deals with the tools and techniques for carrying out the plans” (ANON. 1966). Technology is a wider concept than technique. Each production technol- ogy requires inputs appropriate to it. These inputs can then be utilized by means of several techniques (YUDELMAN 1971, p. 38-39). If technology is divided into land-saving and labour-saving technology (HEADY 1949, p. 296), technique is closer to labour-saving technology (UPTON 1976, p. 201). 174 In terms of production, technological change can be divided into intro- duction of new products, or product innovations, and into new production methods, which are called process innovations. Process innovations can be further divided into introduction of a new means of production and improve- ment of the properties of an older means of production (WILLER 1967, p. 28, UPTON 1976, p. 201). UPTON (1976, p. 201) has defined process innovation as any adopted improvement in the method of production which reduces average costs per unit output at constant input prices. Alternatively, this implies an increase in the average productivity of at least one resource. This study deals mainly with process innovations. New products are not as significant for agriculture as they are for industrial production. Product innovations in agriculture largely represent changes in product quality. Economics has presented several definitions of technological change which differ from each other only in that they focus on different aspects. According to KENDRICK (1961), technological change can be defined as a change in total factor productivity. His starting point is shown in the equation Qo = w OL + r OC, where w 0 is the average wage at time zero and r 0 is the average return to capital at time zero. Changes in total factor productivity from time 0 to time 1 can be calculated by using constant weights and by calculating change as a function of changes in labour and capital in the following way: S' = A (w 0 tl + r„ p 1). Vo Lo '-o In this equation the coefficient A, which characterizes total factor pro- ductivity, represents technological change. Abramowitz (1956) has also used an index based on total factor produc- tivity as his starting point when calculating a factor which he calls residual and which corresponds to technological change. Presented mathematically, Abramowitz’ residual is calculated in the following way: • A I dQ dL , dCresidual = - a<; -j- “b 0 —. where = proportional change in output, 1 = proportional change in labour, = proportional change in capital, ao = labour’s share of income in a base period, b 0 = capital’s share of income in a base period. 175 LEONTIEF (ref. DOMAR 1961, p. 709-710) in turn has defined technologi- cal change as a weighted average of the relative changes of all input coeffi- cients (in accordance with the input-output method) between two points in time. However, in economics generally and also in this study, technological change is defined as a shift in the production function. SOLOW (1957, p. 312) has described technological change ”as a shorthand expression for any kind of shift in the production function”. This definition is based on the idea that technology is ’’embodied” in the production function and can be expressed in its terms. Production function Q = f(Xb X 2,..., where Q = output, X; = factor of production affecting output through production process (i = 1, 2,...,n), shows how production is carried out, i.e. the technology by means of which the production process operates. The parameters of the production function indicate the technology of production. Technological change is only a change in these parameters .Thus defined, technological change is also a change in the productivity of one or more inputs. In this way technological change is also a shift in the production function (NIITAMO 1969, p. 1-2). Presented in a slightly wider mathematical sense, the relation between inputs and output can be described as output vector (Q) through transforma- tion of input vector (X): Q = T(X). T, which in system theory represents the so-called transformation operator, expresses the way in which vector X is transformed into vector Q. This vector indicates the technology by means of which the production process takes place (NIITAMO 1969, p. 11). The shift in the production function has been called both technological change (e.g. DOMAR 1961, LAVE 1966, BROWN 1968, IHAMUOTILA 1971, UPTON 1976) and technical change (e.g. SOLOW 1957, ROUHIAINEN 1972, HEERTJE 1977). German literature in particular has used the term technical progress - technischer Fortschritt (e.g. WILLER 1967, FLECK 1973). HEERTJE (1977, p. 3) has stated that the term technical change may in its broadest sense mean a shift in production function. In this study, however, a shift in the production function is called technological change. 1.2. Characteristics of technological change Technological change can be divided in several ways according to its characteristics. In this study, as in ROUHIAINEN’s (1972) and NIITAMO’s (1969) studies, the classification presented by BROWN (1968) is used. 1. The efficiency of a technology is changed when a given combination of inputs produces a quantitative change in output. The characteristic efficiency deals only with the relationship between inputs and output. It does not affect 176 the relationship between inputs. Neither is it connected with the relationship between the change of output and the change of inputs. Fig. 1 shows the simplest presentation of change in the efficiency of a technology: When two technologies or production methods A and B (Fig. 1) require the same inputs, we can state that technology B is more efficient than technology A at all input quantities, because B lies ’’above” A. 2. Technologically determined economies of scale. Technological progress can alter the way in which inputs are transmitted into output in such a way that the production process formerly characterized, for example, by decreas- ing returns is now characterized, say, by constant returns, while the scale of operations of the firm remains unchanged. This characteristic of technology is presented graphically in Fig. 2. Fig. 2a describes decreasing returns to scale when output moves from Xt to X 3 [X3 >X2 > Xi, (X 3 - X 2) = (X 2 Xi)]. When output grows from X t to X 2, a smaller increase in labour and capital is required than when output is increased form X 2 to X 3. Examining Figure we can suppose that a technological change has occurred and a new configuration of isoquants indicates increasing returns to scale at the same input levels as in Fig. 2a . 3. The capital intensity of a technology varies when the ratio (L:C) between the inputs changes as a result of a proportionally different change in the productivity of the inputs, i.e. the origin of the change is technical (NIITAMO 1969, p. 23): Fig. 1. Change in the efficiency of a tech- nology. Fig. 2. A technologically determined change in the degree of re- turns to scale. Fig. a describes decreasing returns to scale and Fig. b describes increas- ing returns to scale. 177 In Fig. 3, the technologies represented by the X’ isoquants are more capital intensive than those denoted by the X isoquants. The marginal rate of substitution between capital and labour is smaller and the marginal product of capital compared with that of labour is higher in the X’ technology than in the X technology. If a unit of labour is added to both production processes, a smaller amount of capital will have to be withdrawn from the X’ process than from the X process. 4. The ease with which capital is substitutedfor labour changes when e.g. a certain effect of capital change on the quantity of production can be replaced by a different change in labour. This is closely linked with the declining marginal rate of substitution (c.f. Figs. 2 and 3) between labour and capital. A gradual substitution of capital for labour leads to a continuously changing rate of substitution. NIITAMO (1969, p. 13-14) has described this with parameters by means of the so-called elasticity of substitution. We come to this after first defining the marginal rate of substitution, R, which is in fact the ratio of marginal profitability of capital to that of labour. Hence, d 2 R = a§ - where Q output, C = capital and L = labour. After this, the elasticity of substitution (a) can be defined in the following way du ° = ik’ whenu =h- R The elasticity of substitution measures how fast the marginal rate of substitution changes when substitution is continued. The elasticity of sub- stitution can take any value between zero and infinity, always being positive (BROWN 1968, p. 18). The larger the curvature of the isoquants, the smaller the elasticity of substitution. In Fig. 4a the elasticity of substitution is zero and in Fig. 4b it is infinite. The so-called question of complementarity (NIITAMO 1969, p. 14) brings another problem into the discussion of the fourth characteristic of technolog- ical change. Here a certain type of capital requires only a certain type of Fig. 3. Different capital intensities of a technology. The tech- nologies represented by the X' isoquants are more capital intensive than those denoted by the X isoquants. 178 labour. Inputs make each other complete. In agriculture this problem arises especially in tasks requiring great skill. The four main characteristics of technological change have been presented above. Based on them, we can further define the ’’neutral” and ”non-neutral” technological changes. A neutral technological change affects labour and capital in the same way (Fig. sa).5a ). A neutral change is caused either by a change in the efficiency of production or in the rate of returns. On the other hand, a non-neutral change affects the production function, i.e. it alters productivity relations and the rate of substitution in such a way that the process becomes for example more labour-saving (Fig. sg). A non-neutral technological change is caused by alterations in the intensity of capital and in the elasticity of substitution. 2. How technological change occurs 2.1. Forms of technological change A technological change can be either embodied or disembodied, accord- ing to its form (SOLOW 1962, p. 216). This division is based on the idea that the effects of technological changes are on the one hand tied to new capital inputs, and on the other hand a result of improvement in the technical relationships between known inputs. In order to be possible a technological change in the first category requires, introduction of new capital assets either in the form of increased net capital or replacement investment. Without investment to modernize machinery, improved technique merely represents an unused chance to achieve a higher productivity (SALTERS 1960, p. 63). Fig. 4. Extreme values of the elastic- ity of substitution. In Fig. a the elasticity of substitution is zero and in Fig. b it is infinite. 5. A neutral (a) and a non-neut- ral (b) technological change. 179 If a technological change tied to capital is examined together with the durability of capital inputs, more information is gained about this type of change. Short-term capital inputs, which are used during one production period, can be continuously applied with the latest know-how. With long- term capital inputs, which are used for several production periods, the problem of aging is crucial. Long-term means of production that are already laid in and designed for a certain function, such as machines and buildings, can only rarely be applied with the latest know-how, sometimes the applica- tion may not be successful at all. A disembodied change which is independent of capital mainly raises the quality of labour and alters organization. Such changes provide a chance to increase production by the same inputs as before without requiring replace- ment investment. Promotion of vocational skills and experience from a continuous flow of a production process are the basis for this type of technological progress. Change independent of capital can only happen if the people in the production process have a higher level of technical know-how during period t + 1 than during period t (WILLER 1967, p. 33). In the first years of research on technological change, SOLOW (1957) and several of his followers thought the effects of capital on the growth of productivity were insignificant and therefore did not require more thorough study. Later studies have, however, found that embodied and disembodied technological changes have to be examined simultaneously (INTRILLIGATOR 1965, p. 65-70). This is also implied if the term embodied is also used for labour (NIITAMO 1969, p. 16). Then technological change is embodied in the labour force, e.g. in the form of increased working skills. This type of technological change can be embodied simultaneously in both labour and capital. In this situation disembodied changes in technology are mainly organizational as for instance a more efficient use of an existing building, thanks to better planning, etc. In the long run, technological progress independent of capital is not as efficient as progress dependent on capital. Improvements in the quality of the labour force and of the organization approach their limit values unless capital changes. WILLER (1967, p. 23) has divided technological change into induced and autonomous change. An induced change is connected with economic factors and can be regarded as an endogenous variable in terms of production. Such economic factors include a) relative price changes of inputs in the long run, b) learning and experience from the production process and c) investments in trading and research (HEERTJE 1977, p. 174). An autonomous change is independent of economic factors and can be regarded as an exogenous variable. ARROW’S (1962) analysis of the ”learning-by-doing” phenomenon also led to the same classification. Arrow’s starting point was the idea that a substantial part of technical development is not exogenous in view of the enterpreneur and the enterprise. It is instead created within the enterprise by the experience originating from its own production process. In agriculture, technological changes can be classified in the following way: 1) biological, 2) mechanical and 3) organizational changes (HEADY 180 1949, p. 296-297, OTT 1959, p. 302, WILLER 1967, p. 116). Biological changes mean better plant varieties and animal breeds. Innovations in the manufacture and application of inputs to increase output, for example new fertilizers, feeds and concentrates, are also biological changes (WEINSCHENK and MEINHOLD 1969, p. 91). Biological changes have a physiological effect on total output. They raise the productivity of land or the yield per animal. Mechanical changes refer to machines and equipment which compensate capital for labour but do not alter the physiological output of plants and animals. Changes having both biological and mechanical effects are called biological-mechanical (HEADY 1949, p. 297). In general it can be stated that a biological technological change is usually a substitute for land and a mechani- cal technological change is a substitute for labour (WEBER 1973, p. 57). In addition to biological and mechanical technological changes there are also organizational changes in agriculture. These changes are mainly con- nected with the form, structure and size of the enterprise, management and personal questions (SCHAEFER-KEHNERT 1961, p. 218). The agricultural enterpreneur plans the use of inputs in accordance with the goals he sets. Production and marketing of products have to be organized to carry out a production process. If the provisions for production and marketing change essentially, they have to be adapted to meet the new situation. The greater the applicability of new technological inputs in agriculture the higher are the demands on the farmer as manager and organizer of the enterprise. As it is very hard to distinguish from other development, organizational change is usually not examined alone. In most research it is included in biological technology (e.g. WESTERMARCK 1973, p. 15, WEBER 1973, p. 57). In these cases the effects of technological change have been the starting point. On the basis of this, agricultural technology could be classified in the following way (HAYAMI and RUTTAN 1971, p. 44); Agricultural technology 1. A substitute for labour 1.1. Mechanical technology 2. A substitute for land 2.1. Chemical technology 2.2. Biological technology The effects of technological progress on production can be described as follows (WILLER 1967, p. 15): a) Saving in the use of inputs b) Increase in production volume c) Diversification of product range d) Improvement in product quality e) Replacement of old products with new ones Saving in the use of inputs is related to the tendency of technological progress to lower costs. A certain quantity of output is produced with less labour, land or capital, or the same amount of input creates a larger output. The inputs saved can remain as such or they can raise the volume of output in the original use. They can also be transferred to another branch of produc- tion, in which case they increase the volume of production of either com- pletely new products or of those previously manufactured. In this way technological progress can lead to saving, widening of the production base and of the product range. Technological progress may also improve the quality of a product. Although technological changes are usually examined with regard to increased output, it must be noted that they can also reduce losses or insecurity and risk. These changes are ultimately reflected in the output as well. 2.2. Different trends in technological change The period of technological change in agriculture has been described as the ”age of substitutability” (WEINBERG 1978) for some time. New tech- nologies have made it possible to replace scarce and expensive inputs with relatively more abundant and inexpensive ones. A new technology is not always a substitute for land or labour; it often acts as a catalyst in making substitutability between inputs easier. The scarcest input can be used at maximum efficiency and this results in the highest possible output (HAYAMI and RUTTAN 1971, p. 44). Technological progress depends on the preconditions set by the economic and social circumstances of the country. Technological change has occurred in different ways in different countries. The differences between the tech- nologies become obvious when the productivities of agriculture in different countries are compared (Figs. 6 and 7). 2 Fig. 6. Agricultural productivity in some Western countries in 1880-1970, logarithmic scale (RUTTAN et al. 1978, ref. WEINBERG 1978). 181 182 In Fig. 7 the diagonal lines represent constant land/labour ratios and the numbers in parentheses are percentage ratios of agricultural workers to the total economically active population. As illustrated in Figs. 6 and 7, the U.S.A. and Japan represent the extremes of technological progress in the so-called Western countries. They are therefore well suited to analysis. In Japan the inelastic supply of farm land has led to a rapid development of land-saving biological technology. In the U.S.A., on the other hand, a scarcity of labour has led to greater use of machines and mechanical technology. These opposite bases for growth in productivity can best be understood as dynamic adaptation to changing prices of inputs. Although the cost of human labour has no doubt been a decisive factor in the mechanization of agriculture in the U.S.A., other effects of mechaniza- tion should also be stressed in this connection. According to SCHERTZ (1968, p. 3), mechanization helps to 1) accomplish tasks more carefully, 2) make the work faster, 3) create inputs not previously used and 4) accomplish tasks which were not possible with traditional production methods. Inputs representing under mechanical technology, e.g. machines and equipment, are often indivisible and have a long working age. Their use is most profitable in larger enterprises, when fixed costs per product unit decrease. See Fig. 8. Fig. 7. International comparison of labour/output and land/output ratios in situations described by different land/labour ratios in 1970, log. scale (YAMADA and RUTTAN 1975). 183 Adapting mechanical technology to agriculture makes it possible to manage larger production units (cf. e.g. TORVELA and MÄKI 1974, p. 71). As a result, farms in the U.S.A. are very large on average. In Japan the supply of land has been inelastic and the price of land has increased in relation to wages. It has not, therefore, been economically feasible to replace labour with machines. On the other hand, new potentials, which resulted from the steady fall in fertilizer prices in relation to the price of land, were utilized thanks to progress in biological technology. This led primarily to the improvement of plant varieties to give higher yields and make better use of fertilizers. The intensive increase in the amount of fertilizer used in Japan during the past few decades reflects not only farmers’ adaptation to relatively lower fertilizer prices but is also a result of the development of new plant varieties by Japanese agricultural research. These varieties make better use of the increased amounts of fertilizers (HAYAMI and RUTTAN 1971, p. 159). The effect of the prices for means of production on the progress and choice of a technology is shown in Fig. 9 in the case of fertilizers. In both 1880 and 1960 farmers in the U.S.A. used less fertilizer than those in Japan (Fig. 9). However, in spite of the enormous differences in both physical and institutional resources, the relationhip between these variables has been almost identical in these two countries. When the price of fertilizers decreased in relation to other inputs, both Japaneseand American researchers reacted by improving crop varieties to correspond better to reduced fertilizer prices. The Americans have always been some decades "behind” the Japanese in the process, because the price of land was lower in relation to that of fertilizers. This meant that yieldincreasing technology was valued less in the U.S.A. than in Japan. It is possible to find the same process in cross section material pertaining to mechanical technology. Variations in tractor horsepower per worker are to a very large extent a result of the price of human labour in relation to the price of mechanical labour (Fig. 10). When wages increase in countries where there are small farms, such as Japan, it is possible to introduce mechanical technology within the limits set by the field area of the farm (YAMADA and RUTTAN 1975) Fig. 8. Mechanical technology and size of enterprise. 184 Fig. 9. Fertilizer input per arable land area (hectares) in relation to the price ratio between fertilizers and land in the U.S.A. and Japan in 1880-1960 (hayami and RUTTAN 1971, p. 127). Fig. 10. Tractor horsepower per male worker in relation to the ratio between the prices of machines and human labour in 1970, log scale. 185 The increase in the price of fertilizers in relation to the price of land, or the rise in the price of labour in relation to the price of machines has caused changes in biological and mechanical technology. Thanks to cheaper and more profitable new technology, farmers have substituted fertilizers for land and machines for human labour. The technological differences and the different trends correspond to the special features of each country. Farmers, researchers and the agricultural industry and services, all influence tech- nological development (YUDELMAN et al. 1971, p. 40). It appears that during the past two decades as wages increased rapidly in Japan and land prices rose in the U.S.A., the models for technological change have approached each other in these two countries. Both seem to approach the European model of technological change, in which output per worker and per hectare increase at about the same speed. 2.3. The effect of technological change on the optimum level of production To study the effect of technological change on the optimum level of production we can start from a simple example about technological improve- ment, such as that presented in Fig 11. If the technologies or production methods A and B require the same inputs, then from the producer’s point of view technology B is more profitable than technology A. Method B gives a higher level of output for each level of input. The effect of a technological change on the optimum level of production depends upon the manner in which the change affects total output. If the technological change is such that marginal product for a given level of input increases, it is profitable to expand the quantity of the input used. For example in Fig. 12 the marginal product has been increased at each level of input by a technological change. Hence, as the value of the marginal product has grown as a result of technological change, it pays the producer to increase the amount of input X! used from 10 to 15 units. Fig. 11. Improvement in technology. 186 It is possible, on the other hand, for a technological change to increase the total product for some input levels but not to increase the marginal product on these levels. The marginal product of 20 inputs, for example, might be the same for both production methods. However, the total production may be larger with the new method than with the previous one. In this situation the value of the marginal product remains equal for both production methods, and the level of input at which the marginal product equals price is unchanged. Although it is profitable to increase production, it does not pay to increase the quantity of the input used (BISHOP and TOUISSAINT 1958, p. 52). The producer will not approve of a technological change unless he expects its introduction to lead to a reduction in costs per unit at the output at which he expects to operate. Since most innovations involve extra expenditure, total costs often grow at lower levels of output as a result of a technological change. A typical cost situation facing the producer planning a change in a production method is presented in Fig. 13. TC] represents the total cost in relation to output when the original method is used (Fig. 13). TC2 represents the total cost curve after the Fig. 12. Technological change and the maximization of net revenue. Fig. 13. Effects of a technological change on production costs. 187 technological change, when a new production method is used. The total cost of a new technology exceeds the total cost of the old method until a level of production OM is obtained. At higher levels of output the new method is more profitable. The optimum level of inputs is defined by the marginal product and marginal cost as based on the production function. The effect of a technologi- cal change on the optimum use of inputs depends on the quality of the change. A neutral technological change does not affect the form of the production function. In other words, the curve as such moves upwards when MP and MC also remain constant (Fig. 14). A neutral technological change, therefore, does not affect the optimum use of the inputs. A non-neutral technological change, on the other hand, alters the shape of the production function. The value of MP changes simultaneously. After the change, the optimum intensity will be either at the upper or the lower level depending on the point where the condition MP = MC is valid. Technological change can also occur in production that manufactures an input. This change usually lowers the price of the final product. Fig. 14 will be studied below. There the optimum intensity of X; is X;0 . We assume that the price of input X; has dropped as a result of the technological progress mentioned. The marginal cost (MC) then decreases to value MC’ (Fig. 14), which corresponds to marginal product MP’ of equal quantity. The intensity level of input X; has thus risen to Xn- There has been a simultaneous increase in production. 3. Measurement of technological change 3.1. Different lines of measuring In measuring a technological change we are interested in the overall effects of the change and especially in determining its characteristic features Fig. 14. The effect of the change in the ratio between the input price and the final product on the op- timum intensity level of input X,. 188 and in assessing the effect of each of them. The methods for measuring technological change can be divided into two main classes: methods based on production function and those based on index figures (HEERTJE 1977, p. 193, ROUHIAINEN 1972, p. 15). In the methods based on production function, either the transfers of the production function are measured or else a correction required by a technological change is made in the building of the production function. When examining the change in terms of index figures, the technological change is measured by means of indices of inputs and output. The division of measuring methods into these main types is not entirely unambiguous. Measuring methods based on indices are often used in studies on production functions. In principle production function approach is only a mathematical description of measuring method based on indices. 3.1.1. Measuring methods based on a production function When studying measurement of a technological change with regard to the construction of a production function, we start with the following equation Q= f (L, C, A), where L = labour, C capital and A = the part which cannot be explained by the variables L and C, or the residual. Measuring methods based on production function can be divided into traditional and ’’service-flow” methods (NIITAMO 1969, p. 4). Traditional measuring methods are aimed at measuring transfers of the function by adding to the model those variables that are supposed to explain a technological change. This method is based on the fact that technological change is included in the residual. It must be emphasized in this connection that the residual or the unexplainable part may, in addition to the technologi- cal change, include: 1) measuring or aggregation errors, 2) errors in the estimation of parameters, 3) errors in the hypothesis of the function and 4) errors caused by exclusion of one or more variables (ROUHIAINEN 1972, p. 15). In the traditional measuring methods, certain substitute delineators for labour and capital input are approved and the residual is divided each time in an analytically interesting or suitable way. In such cases the inputs are measured without regard to their quality. This is the same as assuming the homogeneity of the inputs (IHAMUOTILA 1971, p. 69). NIITAMO (1969, p. 4) presents the ’’instrumental model” as a more advanced way of traditional measuring: Q = f (L, C, H, V,...,X, e). Labour and capital inputs are measured in some ordinary physical units, and the part which cannot be explained by these variables will be analysed and divided into those factors affecting the quantity of output that the 189 decision-maker can use when he wants to alter production. Among such factors are variables describing effects of change in education and of moder- nization in machinery. In the ’’service-flow” methods, output is always the sum of the inputs used. Qualitative changes in, say, workers and machines should then be reflected as a corresponding change in the labour or capital input concerned. The inputs used are then measured in productivity units. In the service-flow method the residual is regarded entirely as an error in measuring which, in principle, can be made infinitely small. If the inputs are corrected carefully, no errors occur in the measuring and aggregating of inputs, the estimating method and the functional form are correct and all the variables are included, there should be no residual at all. The service-flow method allows only constant returns to scale, because in this method the correction due to technological change has been made through input variables and a corres- ponding quantity of change is reflected in the output (NIITAMO 1969, p. 5). In contrast, increasing and decreasing returns to scale are possible with traditional measuring methods. The greatest problem in the use of service-flow methods is how to measure the input quality. It is hard to define a unit of productivity for many inputs that would be unambiguous and would allow combining of qualitative changes with labour and capital inputs. In measuring methods based on production function the basic problem can be presented as in Fig. 15. Fig. 15 shows that the quantity of output can in principle change in two ways. The change may occur along the production function (A), which requires an increase in inputs Xio - X;i, or as a transfer of the production function (B). In practice (C) is probably the most common. Here the rate of input use increases and we also move to an "upper" production function. When a production function is estimated from data, estimates are Fig. 15. Effect of technological change on production function. 190 obtained for the parameters of the function. These estimates are constants. This means that they indicate the state in which the production technology exists but they say nothing about change in it. The problem behind the measurement of a technological change is thus how the increased output should be divided - and how it can be divided - between the increase in the use of inputs and technological progress. In Fig. 15 the problem is how AQ can be divided between the components AQj and aq 2 . 3.1.2. Measuring methods based on indices A technological change can also be measured by different kinds of productivity indices. Such indices are either partial or total depending on whether the increase in output is calculated for one or for all inputs (HEERTJE 1977, p. 193). Output per unit of labour is a common measure of partial productivity. This partial index is not, however, a good measure of technological change, because it does not take into consideration substitution of the inputs caused by changes inrelative prices. Because the price of labour has also increased in relation to the price of capital in agriculture, the productivity of labour gives the technological change too high a value. This rate also rises faster than technological change does in reality (ROUHIAINEN 1972, p. 19). The index based on total productivity is calculated from the relation between the output index and the indices of all inputs. The total index is calculated either from arithmetic or geometric averages. When arithmetic values are used, the output is divided by the weighted sum of the input indices, whereas the geometric values are presented in logarithmic form (HEERTJE 1977, p. 193). When indices based on total productivity are used, all changes in output are explained by technological change. The greatest problem in the measuring method based on total productiv- ity is how the inputs and outputs should be aggregated. Because changes in the relative prices should not distort the index derived for total productivity, price changes should be eliminated. To solve this problem Laspeyres or Paasche indices or versions of these, such as Fisher’s and Edgeworth’s indices, are normally used (IHAMUOTILA 1971, p. 20, FLECK 1973, p. 89-91). In the Laspeyres index, O. = sEs3l 2poqo where Q = index of gross output, p = price of a single product. q = quantity of a single product, 0 = base year, 1 = year studied, the prices from the base year are used throughout the research period. The base year can be any year within the period studied (IHAMUOTILA 1971, p. 16). 191 In the Paasche index, o„ = Mv/2(po + p.) ’ where the average prices for the base year and for the comparison year are used as weights (FLECK 1973, p. 91). 3.2. Some methods for measuring technological change 3.2.1. Arithmetic and geometric indices Abramowitz’ arithmetic (ABRAMOWITZ 1956) and Solow’s geometric index (SOLOW 1957) can be considered the basic methods for measuring technological change. Both are typical measuring methods based on produc- tivity indices. In the former method the prices of inputs, and in the latter the elasticities of output in relation to the corresponding inputs, are used as weights. Because of these differences in weights, the character of the indices is also different. In the arithmetic index relative prices have to remain constant, and in the geometric index relative shares of returns must be kept constant (LAVE 1966, p. 12-13). The arithmetic index was already studied in connection with the defini- tion of technological change in Chapter 1.1. (p. 174). The equation for the arithmetic index is (LAVE 1966, p. 7): -2l = A (w 0 +r0 -pi-) Vo Lo Vd 192 where Q = output, L = labour input, C = capital input. A = technological change, 0 = base year, 1 = year studied, w = average wages and r = average return on capital. The arithmetic index is quite simple in this form, and therefore it has been used very often, either as such or applied, in the experimental measurement of technological change (e.g. LAVE 1966, KENDRICK 1961). The geometric index applied by SOLOW (1957) studies dependences based on aggregate production function where labour and capital are variables and technological change is a parameter. Solow supposed that the function is homogenous and linear, that the market is in perfect competition and that the technological change is neutral. The function type examined by Solow is Q = A(t) f(C, L). The term A(t) describes technological change, which is a function of time. We can derive the formula below for the calculation of the geometric index (LAVE 1966, p. 11): AA _ Ax Ak ~ä r~ Wc T’ where x= Q/L, k = C/L, A = change in a term between two periods and Wc = elasticity of output with respect to capital. According to this formula, technological change is equal to the change in output not accounted for by changes in labour and capital (LAVE 1966, p. 11). 3.2.2. Production functions The measuring methods based on production functions should be divided into macro- and microeconomic approaches. In the microeconomic produc- tion functions, the latest and most developed technology is generally the starting point (HEADY and DILLON 1961). These functions are used mainly when studying the reasons leading to the development of a technology (HEERTJE 1977, p. 192). Macroeconomic production functions are used in examining the average efficiency of production. Technological progress can then also be negative (LAVE 1966, p. 19). 3.2.2.1. The Cobb-Douglas function The formula for the Cobb-Douglas production function for two inputs is (HEADY and DILLON 1961, p. 75): 193 Q = a L"Cp where Q = output, L labour, C = capital, a, a and fi = parameters. The exponents a and P are the corresponding elasticities of production (HEERTJE 1977, p. 126): «!2 “ = Ä; L dg B = -2-P dc c Technological changes cause changes in the parameters of the production function. In the Cobb-Douglas production function the changes in each parameter (a, a, P) describe a differentkind oftechnological progress (BROWN 1968, p. 39). The change in the efficiency of a technology is reflected only in the term a, as a neutral technological change. A change in the degree of returns to scale is reflected in the variations of the sum a + p. A change in the sum of the parameters a and (3 indicates the degree of returns to scale in the following way: a + P = 1, there are constant returns to scale. When labour and capital are increased by x % (ceteris paribus), output will also rise by x %. «+(s>!, there are economies of scale. When labour and capital are both increased by x % (ceteris paribus), the returns will rise by more than x %. The returns will rise by yx %, when a + (5 =y (NIITAMO 1969, p. 12). a + P < 1, there are diseconomies of scale. Changes in the capital intensity of a technology are seen in the ratio a/(3 . The fourth property of technological change, the rate of substitutability of inputs, cannot be derived from the Cobb-Douglas function, because in this function the elasticity of substitution is 1 with all the combinations of inputs and rates of capital intensity (BROWN 1968, p. 39). The worst deficiency of the Cobb-Douglas function is that it cannot show any changes in the elasticities of substitution and generally does not permit any alternative other than that of complete substitutability (NIITAMO 1969, p. 19). BROWN (1968, p. 38) mentions the following variants of the Cobb-Douglas function in which the variations of elasticities have been taken into account to some extent: Q= L“ G 1 e pL Q = a L° Cp exp(y log L log C) Q = a L“ C? e* e pL . 3.2.2.2. The CES function CES stands for ’’constant elasticity of substitution production function”. This function provides new scope for estimation of technological progress. 194 The Cobb-Douglas function presented above and the Leontief function are special cases of the CES function. In all three functions the elasticity of substitution is assumed to be constant. The difference is that in the CES function elasticity can derive any value between zero and infinity without any other forehand restrictions, whereas in the Cobb-Douglas function the elasticity has been prescribed to be one and in the Leontief function zero (FLECK 1973, p. 165). In designing the formula for the CES function, ARROW et al. (1961) supposed that first, it is a homogeneous first degree function, and second, there is perfect competition both on the product and on the input market. In its basic formula the CES function can be presented in the following way (HEERTJE 1977, p. 127): Q = Y [ÄC* + (1- 6) LT i Y > O 0< Ö -i v > 0. The parameter y in the production function denotes the efficiency of a technology. A proportional change in this parameter causes a proportional change of equal size in the output when all other factors are kept constant. The parameter v shows the degree of returns to scale in the function, i.e. the production function is a homogeneous function of the v:th degree. Thus a neutral technological change is reflected as changes in the efficiency parame- ter y and in the degree of returns to scale v (NIITAMO 1969, p. 42). A non-neutral technological change is associated with variations in 6, the capital intensity parameter, and 0, the substitution parameter. The elasticity of substitution is derived from the substitution parameter through the following transformation: » =t4 The maximum level of the elasticity of substitution infinity makes the minimum of the parameter Q = -1. An elasticity of substitution greater than 1 makes the limits of -1 < Q